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Tables of Contents for Noise Analysis of Radio Frequency Circuits
Chapter/Section Title
Page #
Page Count
List of Figures
ix
 
List of Tables
xi
 
Acknowledgments
xiii
 
1. INTRODUCTION
1
10
1 Architecture of an RF Front End
2
3
2 Motivation
5
3
2.1 Noise Sources in RF Transceiver
5
2
2.2 Autonomous versus Nonautonomous Circuits
7
1
3 Overview
8
3
2. OVERVIEW OF EXISTING TECHNIQUES
11
10
1 Perturbation Analysis of a Nonoscillatory System
11
2
2 Noise Analysis of Nonoscillatory Systems
13
2
2.1 LPTV Approaches and Extensions
14
1
2.2 Time Domain Analysis
14
1
2.3 Our Approach
15
1
3 Oscillator Phase Noise Analysis
15
4
3.1 LTIILTV Noise Analysis
16
1
3.2 Timing Jitter Analysis
17
1
3.3 Time Domain Noise Analysis
17
1
3.4 Other Approaches
18
1
3.5 Our Approach
18
1
4 Noise Analysis of Phase-Locked Loops
19
2
4.1 Existing Approaches
19
1
4.2 Our Approach
19
2
3. PERTURBATION ANALYSIS OF STABLE OSCILLATORS
21
32
1 Mathematical Preliminaries
21
2
2 Perturbation Analysis Using Linearization
23
9
2.1 Floquet Theory
24
4
2.2 Response to Deterministic Perturbation
28
2
2.3 Response to Stochastic Perturbation
30
2
3 Nonlinear Perturbation Analysis for Phase Deviation
32
6
4 Example
38
15
4.1 The van der Pol Oscillator
38
3
4.2 Forced van der Pol Oscillator Equation
41
3
4.3 Perturbation Analysis of the Forced van der Pol Oscillator
44
9
4. NOISE ANALYSIS OF STABLE OSCILLATORS
53
38
1 Stochastic Characterization of Phase Deviation
53
16
1.1 Kramers-Moyal Expansion and Fokker-Planck Equation
55
6
1.2 Solution of the Phase Deviation Equation
61
8
2 Spectrum of Oscillator Output with Phase Noise
69
4
3 Phase Noise Characterization for Oscillator
73
3
3.1 Single-Sided Spectral Density and Total Power
74
1
3.2 Spectrum in dBm/Hz
75
1
3.3 Single-Sideband Phase Noise Spectrum in dBc/Hz
75
1
3.4 Timing Jitter
76
1
4 Noise Source Contribution
76
 
5 Numerical Techniques for Phase Noise Characterization
17
66
5.1 Time Domain Technique
77
2
5.2 Frequency Domain Technique
79
4
6 Examples
83
8
6.1 Generic Oscillator
83
2
6.2 LC Tank Oscillator
85
2
6.3 Ring Oscillator
87
3
6.4 Relaxation Oscillator
90
1
5. NOISE ANALYSIS OF NONAUTONOMOUS CIRCUITS
91
26
1 Mathematical Preliminaries
92
1
2 Cyclostationary Approach
93
1
3 Response of a Noiseless Circuit to Input Signal Phase Noise
94
4
4 Extension to General Noise Analysis
98
2
5 Amplitude Noise Characterization of Oscillators
100
1
6 Modification to Existing Noise Analysis Techniques
101
11
6.1 Time-Domain Technique
103
1
6.2 Frequency-Domain Technique
104
8
6.2.1 Noise Propagation Through Linear Time-Varying System
105
4
6.2.2 Evaluation of System Transfer Function
109
3
7 Examples
112
5
7.1 Passive Mixer
113
1
7.2 Active Mixer
114
3
6. NOISE ANALYSIS OF CIRCUITS WITH MULTITONE INPUTS
117
30
1 Mathematical Preliminaries
118
1
2 Spectrum of Nonlinear Mixing of Two Tones
119
2
3 Multirate Analysis of Circuits with Multitone Excitations
121
5
4 Noise Analysis of Circuits Driven by Multitone Excitations
126
8
5 Numerical Techniques
134
10
5.1 Propagation of Noise Through a Linear Quasi-Periodic Time Varying System
135
6
5.2 Derivation of the Form of Transfer Function
141
3
6 Examples
144
3
7. NOISE ANALYSIS OF PHASE-LOCKED LOOPS
147
18
1 Introduction
147
1
2 PLL Noise Analysis
148
6
2.1 Solution of the PLL Phase Equation
151
2
2.2 PLL Output Spectrum
153
1
3 PLL Examples
154
4
3.1 PLL without loop filter
154
1
3.2 PLL with first order filter
155
1
3.3 Charge Pump PLL (CPPLL)
156
2
4 Experimental Results
158
7
8. CONCLUSIONS AND FUTURE DIRECTIONS
165
12
1 Conclusions
165
1
2 Noise Models for Circuits Driven by Multitone Excitations
166
1
3 Extensions to Non-White Noise Sources
167
1
4 Behavioural Level Noise Simulation
168
9
Appendices
177
1
Definitions and Solution Techniques of SDEs
177
 
1 Mathematical Preliminaries
177
1
2 Itô Integrals
178
2
3 Stochastic Differential Equations
180